Finding a time that is free is easy. Finding one people accept is a different problem, and it is the whole of this.
Intersect six free/busy feeds over a fortnight and you get dozens of openings. Most of them are unusable for reasons no calendar records. It is twenty past six in the morning in Vancouver. It is somebody's lunch. It is ten minutes after a three-hour workshop, so the person the decision rests on will arrive not having stood up since breakfast. It is Saturday. It starts in eighteen minutes. Every one of those is technically free, and a tool that offers them is a tool people stop opening — because "the calendar said it was free" is not a defence anybody has ever accepted.
So the times are worked out before any calendar is read. That order is the design. From three things that need no calendar at all — who is coming, what zone each of them lives in, and what hour of their own day it is reasonable to ask for — the server produces a numbered list of every half hour that is inside all of their working days, off their lunches, off the weekend, and far enough ahead that somebody could still move something. Only then are the calendars read, and all that remains is to cross out what is taken.
That order also settles who does the arithmetic. The list goes to the model already numbered, so the model has no times to invent: it can strike one out, and that is the only thing it can do to the list. Removing too much is visible — the document states how many were left and why — while adding one is not, because a proposed time nobody checked looks exactly like a proposed time that was. The crossing-out is then done again in code, from the same busy blocks, and a finished document naming a time the arithmetic did not clear is rejected rather than published.
Every local time in it is computed per instant in that person's own named zone, never from a stored offset. An offset is a fact about a moment, not about a place, so code that remembers "Lisbon is one hour ahead" is right for seven months of the year and puts the meeting an hour out for the rest. The same discipline covers the fortnight each autumn when Europe has changed and the United States has not, which is the week a hand-rolled converter is wrong every single day.
Then there is fairness, which is the part that decides whether anybody turns up. Rank by the earliest free slot and the same person takes the early morning every week, and that person is usually the one whose decision everybody is waiting for. So the ranking minimises the worst case rather than the average: the time that is fine for five people and brutal for one loses to the time everybody can actually make. The document shows what each option asks of whom, in their own clock, so a choice that is convenient for most of the room cannot be sent as though it suited all of it.
What it refuses to claim matters as much as what it proposes. A calendar that could not be read is named, with the reason, and nothing is presented as free for everyone while one is missing — because "assume they can make it" is the step that produces a meeting the one required person cannot attend, and the person who forwarded it is the one who looks careless. A name in the request that belongs to nobody in your workspace is dropped and counted, never guessed at: their address is not carried anywhere, so no calendar outside your organization is read, and there is no later permission check to forget.
And it stops before the invitation. Writing to a calendar needs a human decision, and the honest version of that decision has to show you the time it is about — which the approval could not, because it would have to be given before the calendars were read. A duplicate invitation sitting in six people's calendars is not something an apology fixes. So the document ends with the times, in everybody's own clock, and a section saying plainly that nothing has been booked. Sending it is the ten seconds you keep.